Question

What is the number of atoms in a face centred unit cell?
A.2
B.4
C.6
D.3

Answer 1

Hint: The smallest repeating unit in a crystal is termed as unit cell. There are many types of unit cell, primitive cubic unit cell, body centred cubic cell and face centred unit cell.

Complete step-by-step answer:
A face centred cubic unit cell has atoms at all the corners and at the centre of all faces of the cube. In a cubic unit cell, each corner atom is shared between 8 unit cells.
In a face centred unit cell, 8 atoms are present in the corner. So, the atoms contributed by corner atoms can be calculated as follows:

8 corner atoms$ \times $$\dfrac{1}{8}$atom per unit cell=$ 8 \times \dfrac{1}{8} = 1$ atom

There are 6 face centred atoms present in the face centred unit cell and each face centred atoms are shared by two unit cells. So, the atoms contributed by face centred atoms can be be calculated as follows:

6 face-centred atoms$ \times $$\dfrac{1}{2}$atom per unit cell=$ 6 \times \dfrac{1}{2} = 3$ atom

So, the total atoms of the face centered cubic cell are 4.

Hence, the correct option is B.

Note: Students might be confused about the number of atoms in body centred and primitive unit cells.
In primitive unit cell, 8 atoms present at the corner and each atom is shared by 8 unit cells, so, the number of atoms contributed is equal to $ 8 \times \dfrac{1}{8} = 1$atom
In a body centred cubic unit cell, 8 atoms are present at the corners and one is the centre of the body. We know that 8 corner atoms contribute one atom $\left( {8 \times \dfrac{1}{8} = 1} \right)$ and one body centred atom belongs to only one unit cell. So, the total number of atoms in a body centred unit cell is 2.